Potentials and Motion

[Analog_Engine.git] / scripts / TP1 04.12 Harmonic Oscillator.LACE

# Harmonic Oscillator
# A mass m is subject to a force F=-k*r.
# What is the trajectory if the mass starts at position (a,0,0)?
# How much time does it take to pass through zero?
# What is the trajectory if it starts at (a,0,0) with velocity (0,v0,0)?
# Compare to the case including gravity on earth in x direction
# m*x'' = -k*x + 	g
# m*y'' = -k*y (z can be set to 0).

coefficient.1(-1) -> -a    # (a,0,0), has to be negative because x' is negative
coefficient.2     -> k/m_x # k/m for x
coefficient.3(+1) -> v0    # (0,v0,0), has to be positive because y'' is positive
coefficient.4     -> k/m_y # k/m for y, identical to k/m for x
coefficient.5(-1) -> -g     # g

iintegrate x'' -> -x'
iintegrate -x' -> x
   IC: -a
cmultiply (k/m_x, x) -> k/m*x
isum (k/m*x, -g) -> -k/m*x+g
assign (-k/m*x+g) -> x''

iintegrate y'' -> -y'
   IC: v0
iintegrate -y' -> y
cmultiply (k/m_y, y) -> k/m*y
invert (k/m*y) -> -k/m*y
assign (-k/m*y) -> y''

output x -> out.x
output.y -> out.y